sixth grade utah mathematics core (condensed version)
Standard 1: RATIOS & PROPORTIONAL RELATIONSHIPS
- Understand ratio concepts and use ratio reasoning to solve problems
- Understand the concept of a ratio & use ratio language to describe a ratio relationship between two quantities
- Understand the concept of a unit rate associated with a ratio
- Use ratio & rate reasoning to solve real-world & mathematical problems
- Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, plot the pairs of values on the coordinate plan, use tables to compare ratios
- Solve unit rate problems including unit pricing & constant speed
- Find a percent of a quantity as a rate per 100
- Use ratio reasoning to convert measurement units
Standard 2: THE NUMBER SYSTEM
- Apply & extend previous understandings of multiplication & division to divide fractions by fractions
- Interpret & compute quotients of fractions, and solve word problems involving division of fractions by fractions
- Compute fluently with multi-digit numbers & find common factors & multiples
- Fluently divide multi-digit numbers using the standard algorithm
- Fluently add, subtract, multiply & divide multi-digit decimals using the standard algorithm for all operations
- Find the greatest common factor of two whole numbers less than or equal to 100 & the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
- Apply & extend previous understandings of numbers to the system of rational numbers
- Understand that positive & negative numbers are used together to describe quantities having opposite directions or values.
- Understand a rational number as a point on the number line. Extend number line diagrams & coordinate axes familiar from previous grades to represent points on the line & in the plane with negative number coordinates.
- Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line
- Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane
- Find & position integers & other rational numbers on a horizontal or vertical number line diagram
- Understand ordering & absolute value of rational numbers.
- Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram
- Write, interpret & explain statements of order for rational numbers in real-world contexts
- Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation
- Distinguish comparisons of absolute value from statements about order
- Solve real-world & mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Standard 3: EXPRESSION & EQUATIONS
- Apply & extend previous understandings of arithmetic to algebraic expressions
- Write & evaluate numerical expressions involving whole-number exponents
- Write, read & evaluate expression in which letters stand for numbers
- Write expressions that record operations with numbers & with letters standing for numbers
- Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity
- Evaluate expression at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents in the conventional order when there are not parentheses to specify a particular order.
- Apply the properties of operations to generate equivalent expressions.
- Identify when two expressions are equivalent.
- Reason about & solve one-variable equations & inequalities
- Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
- Use variables to represent numbers & write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
- Solve real-world & mathematical problems by writing & solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.
- Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
- Represent & analyze quantitative relationships between dependent & independent variables
- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent & independent variables using graphs & tables, and relate these to the equation.
Standard 4: GEOMETRY
- Solve real-world & mathematical problems involving area, surface area, & volume
- Find the area of right triangles, other triangles, special quadirilaterals, & polygons by composing into rectangles or decomposing into triangles & other shapes; apply these techniques in the context of solving real-world & mathematical problems.
- Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as it would be found by multiplying the edge lengths of the prism.
- Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side jointing points with the same first coordinate or the same second coordinate.
- Represent three-dimensional figures using nets made up of rectangles & triangles, and use the nets to find the surface area of these figures.
Standard 5: STATISTICS & PROBABILITY
- Develop understanding of statistical variability
- Recognize a statistical question as one that anticipates variability in the data related to the question & accounts for it in the answers
- Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape
- Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number
- Summarize & describe distributions
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots
- Summarize numerical data sets in relation to their context:
- Reporting the number of observations
- Describing the nature of the attribute under investigation, including how it was measured & its units of measurement
- Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered
- Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered